Oscillations Definition and 518 Threads

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.

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  1. R

    What do the subscripts fpq and fqp mean in coupled oscillators and waves?

    Homework Statement The following is a question from an old assignment on coupled oscillators and waves: http://img214.imageshack.us/img214/601/question2.jpg The Attempt at a Solution So, I'm a confused about the meaning of the subscripts fpq and fqp. What do they mean? Do fp and fq refer to...
  2. R

    Solve Oscillations (SHM) Homework Statement: 76.7628 N/m & 51.0543 m

    Homework Statement I'm trying to solve this problem: http://img824.imageshack.us/img824/3513/prob1r.jpg The Attempt at a Solution I rearranged the equation T=2π√m/k to find the spring constant: k= \frac{m}{\left( \frac{T}{2 \pi} \right)^2} = \frac{70}{\left( \frac{6}{2 \pi}...
  3. D

    Small Oscillations about the equilibrium point:

    Homework Statement v(x)= (1/x^2) -(1/x) Find the frequency of small osciallations about the equilibrium point Homework Equations The Attempt at a Solution I have so far worked out the equilibrium point is at x=2, to get this i differentiated v(x) and solved it, but could...
  4. P

    Calculating Mass and Gravity on Planet Newtonia

    On the planet Newtonia, a simple pendulum having a bob with mass 1.00 and a length of 195.0 takes 1.40 , when released from rest, to swing through an angle of 12.5 , where it again has zero speed. The circumference of Newtonia is measured to be 51400 . I solved for g using T = 2pi*sqrt(L/g)...
  5. 9

    Why do neutrino oscillations require mass?

    I was reading up on chameleon particles today, and this lead me to reading more about neutrino oscillations - I noticed that at one point it said for oscillations to occur, neutrinos must have mass, there was no explanation to this, but it goes against the standard model. Since I am only young...
  6. H

    Harmonic Oscillations with Escapement [Clock]

    Homework Statement Clock activates escapement every time it passes through the vertical. Escapment under tension from a hanging weight that gives an impulse distance l from the pivot. Energy transferred by this compensates for the energy dissipation due to friction so the amplitude is...
  7. K

    Gas Compression in piston and resulting oscillations

    Homework Statement A cylinder is filled with .1 moles of an ideal gas at STP, and a piston of mass 1.4Kg seals the gas in the cylinder with a frictionless seal, as shown in the figure below. The trapped column of gas has an initial height 2.4. The piston and cylinder are surrounded by air...
  8. J

    Why Does the Restoring Force Use k1x + k2x in Spring Oscillations?

    Looking at the three diagrams we can see that there are three possible situations (a) mass is to the right of eqm (b) mass is at eqm (c) mass is to the left of eqm (eqm = equilibrium) Lets look at position (a) If we consider the tension in both springs: the tension in the spring on...
  9. L

    Superposition of harmonic oscillations

    Homework Statement Find the amplitude and phase shift of the following two superposed harmonic oscillations. Homework Equations x1(t)=3sin(2∏t+∏/4) x2(t)=3cos(2∏t) The Attempt at a Solution Ok normally i would be able to do this, however one oscillation is cos and the other sin...
  10. J

    The link between CP violation and neutrino oscillations?

    I'm trying to understand a bit about CP violation and how it relates to neutrino oscillation. I have a book, "Introduction to High Energy Physics" (Donald Perkins) which says that the probability of observing no change in the flavour of a neutrino is equal to that of an antineutrino of the same...
  11. Doofy

    I have some confusion over neutrino oscillations?

    I'm trying to learn the basic theory of neutrino oscillations at a postgraduate level. I have a few things that are bothering me. 1) All of the papers & textbooks I have looked at start out by just assuming that each neutrino flavour eigenstate is a superposition of the mass eigenstates...
  12. fluidistic

    What Are the Best Approximations for Small Oscillations in Classical Mechanics?

    I'm not sure where to post this question. In classical mechanics many problems are simplified in the approximation of "small angles" or "small oscillations". Wikipedia gives the following criteria or approximations: \sin \theta \approx \theta. \cos \theta \approx 1 - \frac{\theta ^2}{2} \tan...
  13. fluidistic

    Small oscillations, strange springs

    Homework Statement Consider 2 masses linked via 3 springs in this way |----m----m----| where the | denotes fixed walls and the ---- the springs. The length between the walls is 2L and the natural length of each spring is b=L/3. When we move a mass from its equilibrium position, each spring...
  14. M

    Oscillation damped oscillations ? how to calculate energy after t

    Homework Statement 3. A damped oscillator's amplitude dec¡eases from 8 cm to 4 cm in 20 seconds, If the intial energy of the oscillator is 64 J, what is the energy âfter 40 seconds? (Recall: E: (l/2)kA2) Homework Equations not sure how to approach the problem The Attempt at a...
  15. 1

    Variable mass/force oscillations

    Hi, I'm working on a problem that i would like your input on. I have a solution but i would like to see how others would approach it since my solution is more of a hypothesis until we continue with the testing phase. In the most basic form, this project can be described as a hanging container...
  16. T

    The frequency of forced oscillations

    So the frequency of an oscillator is always the same as the frequency of the force, if that force is a sinusoidal function of time. What's the best way to visualize why this is so? And also, why is the frequency of the oscillator in phase with the force if the force is below the resonance...
  17. O

    Simple Harmonic Motion/Energy: Damped Oscillations and Energy Dissipation

    Homework Statement Problem: A 2.0 kg block oscillates up and down on a spring with spring constant 240 N/m. Its initial amplitude is 15 cm. If the time constant ("tau") for damping of the oscillation is 4.0 s, how much mechanical energy has been dissipated from the block-spring system after 12...
  18. K

    Electron Oscillations in a Plasma - trouble with electric fields

    Homework Statement In a cold plasma (neglecting thermal pressure) the background medium is motionless and uniform for the electrons: \rho_e = \rho_{e0} + \rho_{e1} v_e = v_{e1}\hat{z} where ρ is electron density and v is velocity. Subscript 0 denotes a constant value and 1 denotes a small...
  19. A

    Free Oscillations of materials

    Problem A vertical oscillating system consist of three equal springs with elasticity coefficient c , among which a mass m=2kg is suspended.The system oscillates according to the following law of motion x(t)=0,4 cos 4t+0,5 sin 4t , (m) . Determine: 1) The equivalent elasticity...
  20. D

    Neutrino Oscillations at Low Energies

    Hello, I am in the process of learning about neutrino oscillations. I'm looking for some clarification as a google/forum search hasn't helped me. If someone could advise me or point me in the right direction that would be great! So, if you have neutrinos at energies below the threshold...
  21. J

    What is the Frequency of Small Amplitude Oscillations in an Inverted Pendulum?

    Homework Statement A pendulum consists of a massless rigid rod with a mass at one end. The other end is pivoted on a frictionless pivot so that it can turn through a complete circle. The pendulum is inverted, so the mass is directly above the pivot point, and then released. The speed of the...
  22. D

    Period and amplitude of oscillations.

    Homework Statement Block “A” is released with initial velocity v=10 m/s. Find the period and the amplitude of oscillations after inelastic collision of block “A” with block “B”. The mass of block “A” is 2 kg, the mass of block “B” is 2 kg. The spring constants of the springs are 100 N/m and 300...
  23. B

    Spring oscillations determining period of motion

    Hey guys, i can't figure this one out. a mass attached to a spring oscillates with an amplitude of 18cm; the spring constant is k=18N/m. when the position is half the maximum value, the mass moves with velocity v=27cm/s. a) determine the period of motion. b)find the value of mass i...
  24. V

    Oscillations of fluid in a U tube

    Homework Statement We have a U tube, like this one: With the a nonviscous, incompressible fluid at height h at equilibrium. We're interested in finding the frequency of small oscillations about the equilibrium. The tubes have area A (though I'm guessing this falls out in the end) and are L...
  25. C

    Superposition of simple harmonic oscillations

    I know how to add harmonic oscillations on the same axis but i was wondering why can i do it? If i have x1(t)=Asin(w1t +fi1) and x2(t)=Bsin(w2t +fi2), why can i say that the resultant motion is x=x1+x2. Once again I am not interested in the solution because i know how to derive it but how to...
  26. R

    Oscillations, two masses on opposite ends of the same spring

    Homework Statement Two masses, M and 4M, are on opposite ends of a massless spring, sitting on a frictionless, horizontal table. The spring is compressed, and the spring-and-masses system is released from rest. If mass M oscillates with amplitude A and frequency f, then mass 4M will oscillate...
  27. P

    Solving the Differential Equation for Harmonic Oscillations

    greetings Is there any way how to analytically solve the differential equation for harmonic oscillations ? x'' + (kx)/m=0 where m is the mass and k is the spring constant thanks
  28. E

    Swinging mass on a string + Oscillations

    If you have a mass on a string and you spin it in circular motion parallel to the plane of the horizontal floor, is the mass falling under the effect of gravity at all? Is it that during this circular motion, the mass falls a certain height and the tension in the string pulls it back up? Then...
  29. E

    Steady state behavior for a particle undergoing damped forced oscillations

    Homework Statement consider a system with a damping force undergoing forced oscillations at an angular frequency ω a) what is the instantaneous kinetic energy of the system? b) what is the instantaneous potential energy of the system? c) what is the ratio of the average kinetic energy to the...
  30. DevilsAvocado

    Neutrino Oscillations for Dummies

    Neutrino Oscillation for Dummies If someone has the time to answer these questions, it would be much appreciated. According to Wikipedia http://en.wikipedia.org/wiki/Neutrino_oscillation" is of "interest since observation of the phenomenon implies that the neutrino has a non-zero mass"...
  31. L

    Semi-circle with small angle harmonic oscillations

    Homework Statement Consider a uniform semicircular disk of radius R, which rolls without slipping on a horizontal surface. Recall that the kinetic energy of an object is the sum of the translational kinetic energy of the centre of mass (point C) and the rotational kinetic energy about the...
  32. M

    I in: Mechanical Oscillations - Angular freq, Energy of oscillating system

    Dear Collegues, Can you help me to answer theese : Describe the mechanical energy of the oscillating system, with the special interest in the equilibrium and extreme positions. And can u tell me please, that, what is angular frequency in this topic?
  33. T

    Apparent weight lab: oscillations and v(t) graph

    Homework Statement In a lab I collected data for change in apparent weight of a ~1kg mass during an elevator ride. The mass was suspended from the scale by doubled up rubber bands. This caused plenty of oscillations in the data. Can i apply the form mx"(t)+γx(t)+kx(t)=Fcosωt to this situation...
  34. J

    Electric Field/Plasma Oscillations

    Homework Statement Suppose there is a "slab" of plasma in a gas, and let N be the density of free electrons/unit volume. If an external electric field is applied, all the electrons move upwards a distance of x, which produces a thin sheet of unbalanced negative charge -Nex per unit area at the...
  35. L

    Horizontal and vertical oscillations of a loaded spring

    Homework Statement Revered Members, I have attached two images which explain horizontal and vertical oscillations of a loaded spring. In horizontal oscillations the restoring force is taken as F = -kx. But in vertical oscillations the restoring force is taken as F = kdl. Homework...
  36. P

    Physics II forgotten equation (oscillations)

    I am reviewing for a test on oscillations and I have no clue how I derived a formula I used for my homework. Could anyone help me figure out where the equation v=w{\sqrt{A^2x^2}} comes from? Thank you.
  37. M

    Measuring the phase in neutrino oscillations

    Hi, When we talk about neutrino oscillations, the discussion is always about the phase that a particular flavour eigenstate picks up with time. The phase is usually partly geometric and partly dynamic. I have a question about this. How do we measure the phase experimentally? What is the...
  38. Spinnor

    Measuring Neutrino Oscillations in a Solar Neutrino Rest Frame

    If I moved in the rest frame of a solar neutrino would I still measure neutrino oscillations? Thank you for any help!
  39. B

    Solving Parallel Plate Capacitor Pendulum Oscillations

    1. Homework Statement PLEASE DO NOT DELETE THIS POST, MODS, IT MAY LOOK LIKE THE SAME QUESTION AS BEFORE, BUT IT IS NOT, IT IS A TOTALLY DIFFERENT PART TO THE QUESTION. consider a parallel=plate capacitor with square plates of side L and distance d (<<L) between them, charged with charges...
  40. U

    Question about vertical oscillations and energy

    I have a few questions regarding vertical oscillations (not damped). Let's say you have a spring hanging from a ceiling with a mass attached to it. So, for example, if I had a mass attached to a spring and I pulled it down by 10 meters, if mg/k = 5 meters then the amplitude would be 5 meters...
  41. M

    Question about neutrino oscillations

    Hi. I'm a college undergrad (junior year, so basic knowledge of QM but not much else) and I'm reading up on neutrino oscillations. I have a few questions. For neutrinos, which is more fundamental: The mass eigenstates or the flavour eigenstates? In this paper...
  42. D

    Forced Oscillations: +ve Sign of Fcoswt

    In the equation of forced oscillations (given below), ma = -kx + FCoswt, why is that the 2nd term on the right hand side is given the +ve sign. I know that kx should be negative since 'ma' and 'x' are in opposite directions. I can't quite seem to get the gist of Fcoswt being given a +ve...
  43. fluidistic

    Normal modes for small oscillations

    Homework Statement I'm stuck at understanding how to find the kinetic and potential energy matrices such that the determinant |V- \omega ^2 T|=0 when solved for \omega, gives the normal modes (characteristic frequencies?) of the considered system. For example in Goldstein's book for a molecule...
  44. fluidistic

    First steps to understand small oscillations in CM +1 little problem

    Homework Statement I'm trying to teach myself Small Oscillations in Classical Mechanics. So far I've read in Landau, Golstein, Wikipedia and other internet sources but this subjet seems really tough to even understand to me. What I understand is that if we have a potential function that...
  45. G01

    Guitar String Oscillations caught by iphone

    Don't know if this have been posted here yet (anyway I don't see it on GD yet) Anyway, this is pretty cool, even if it isn't a true representation of the guitar strings' motion. The "rolling shutter" effect in the iphone's camera can be used to pick up representations of the sounds being...
  46. K

    What are the conditions for different types of damping in oscillations?

    Homework Statement A mass m moves in one dimension x subject to a restoring force −kx and a damping force −γ[(x)\dot]. What are the conditions for underdamped oscillations, overdamped oscillations, and critical damping? Now, suppose m is 0.80 kg, γ is 1.18 kg/s, and the oscillations are...
  47. M

    Radiation from electron oscillations at plasma frequency?

    Hi, there have been a number of recent papers with regards to radiation from hypervelocity meteor impact, where the authors propose that the radiation originates from self-consistent electron oscillations at the plasma frequency. Some examples: 1) Close et al - Journal of Geophysical...
  48. T

    How Does Damping Affect Oscillation Amplitude and Frequency?

    Homework Statement The drawing to the left shows a mass m= 1.8 kg hanging from a spring with spring constant k = 7 N/m. The mass is also attached to a paddle which is emersed in a tank of water with a total depth of 27 cm. When the mass oscillates, the paddle acts as a damping force given by...
  49. N

    Proton Oscillations: Utilizing Charge for Efficient Space Communication

    We use oscillating electrons to communicate through space due to its charge. Can't we use protons to do the same thing since they also have charge? If yes then how come we don't, is it because they have more mass which would need more energy and thus is less efficient
  50. B

    Oscillations of Covalent Molecules

    Homework Statement Many diatomic (two-atom) molecules are bound together by covalent bonds that are much stronger than the van der Waals interaction. Experiment shows that for many such molecules, the interaction can be described by a force of the form F_{r} = A[ e^{- 2b( r - R_0 )} - e^{ -...
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